In this work we explore how different types of resources are distributed among the states generated by quantum random circuits (QRC). We focus on multipartite non-locality, but we also analyze quantum correlations by appealing to different entanglement and non-classicality measures. We analyze the violation of Mermin and Svetlichny inequalities in order to get a glance at the distribution of nonlocality and genuine multipartite nonlocality. Next, we compare universal vs non-universal sets of gates, to gain insight into the problem of explaining quantum advantage. By comparing the results obtained with ideal (noiseless) vs noisy intermediate-scale quantum (NISQ) devices, we lay the basis of a certification protocol, which aims to quantify how robust is the resources distribution among the states that a given device can generate. We have implemented our non-locality-based benchmark on actual quantum processors with different architectures, in order to assess up to which point they are capable of reproducing the ideal results.